The main purpose of this workshop is to exchange new ideas in strongly correlated electron systems and promote collaborations among researchers at the Perimeter Institute and the University of Illionis at Urbana-Champaign.

Last year, the first joint workshop between the two institutes was held at Urbana-Champaign with focus on topological quantum matter, application of holographic methods in condensed matter physics and Majorana fermions.

This year, Perimeter Institute plans to host the second joint workshop. The topics to be discussed in the workshop include the interplay between symmetry and topology in quantum many-body systems, entanglement in numerical simulations and experiments, quantum phase transitions and criticality.

Electrons moving in a periodic electric potential form Bloch energy bands where the mass of electrons are effectively changed. In a strong magnetic field, the cyclotron orbits of free electrons are quantized and Landau levels forms with a massive degeneracy within. In 1976, Hofstadter showed that for 2-dimensional electronic system, the intriguing interplay between these two quantization effects can lead into a self-similar fractal set of energy spectrum known as “Hofstadter’s Butterfly.” Experimental efforts to demonstrate this fascinating electron energy spectrum have continued ever since. Recent advent of graphene, where its Bloch electrons can be described by Dirac feremions, provides a new opportunity to investigate this half century old problem experimentally. In this presentation, I will discuss the experimental realization Hofstadter’s Butterfly via substrate engineered graphene under extremely high magnetic fields controlling two competing length scales governing Dirac-Bloch states and Landau orbits, respectively. In addition, the strong Coulomb interactions and approximate spin-pseudo spin symmetry are predicted to lead to a variety of integer quantum Hall ferromagnetic and fractional quantum Hall states and the quantum phase transition between them in graphene. I will discuss several recent experimental evidences to demonstrate the role of the electron interaction in single and bilayer graphene.

Allan MacDonald, University of Texas

Majorana State Properties in Semiconductor and Oxide Superconducting Quantum Wires

When proximity coupled to s-wave superconductors, quantum wires can support effective p-wave superconductivity under appropriate circumstances. The p-wave state has Majorana states at the wire ends which can store quantum information. I will discuss some properties of Majorana states formed in oxide and semiconductor quantum wires, including superconducting state phase diagrams as a function of spin-orbit coupling strength, Fermi energy, and external magnetic field strength, and Majorana exchange properties.

Roger Melko, Perimeter Institute & University of Waterloo

Entanglement at strongly-interacting quantum critical points

At a quantum critical point (QCP) in two or more spatial dimensions, leading-order contributions to the scaling of entanglement entropy typically follow the "area" law, while sub-leading behavior contains universal physics. Different universal functions can be access through entangling subregions of different geometries. For example, for polygonal shaped subregions, quantum field theories have demonstrated that the sub-leading scaling is logarithmic, with a universal coefficient dependent on the number of vertices in the polygon. Although such universal quantities are routinely studied in non-interacting field theories, it requires numerical simulation to access them in interacting theories. In this talk, we discuss numerical calculations of the Renyi entropies at QCPs in 2D quantum lattice models. We calculate the universal coefficient of the vertex-induced logarithmic scaling term, and compare to non-interacting field theory calculations. Also, we examine the shape dependence of the Renyi entropy for finite-size lattices with smooth subregion boundaries. Such geometries provide a sensitive probe of the gapless wavefunction in the thermodynamic limit, and give new universal quantities that could be examined by field-theoretical studies in 2+1D.

Robert Myers, Perimeter Institute

Quantum quenches & holography

We employ holographic techniques to study quantum quenches at finite temperature, where the quenches involve varying the coupling of the boundary theory to a relevant operator with an arbitrary conformal dimension. The evolution of the system is studied by evaluating the expectation value of the quenched operator and the stress tensor throughout the process. The time dependence of the new coupling is characterized by a fixed timescale and the response of the observables depends on the ratio of the this timescale to the initial temperature. The observables exhibit universal scaling behaviours when the transitions are either fast or slow, i.e., when this ratio is very small or very large. For fast quenches, we uncover a universal scaling behaviour in the response of the system, which depends only on the conformal dimension of the quenched operator in the vicinity of the ultraviolet fixed point of the theory.

Philip Philips, University of Illinois

Unparticles and Fermi Arcs in the Cuprates

One of the open problems in strong correlation physics is whether or not Luttinger's theorem works for doped Mott insulators, particularly in the pseudo gap regime where the pole-like excitations form only a Fermi arc. I will begin this talk by using this theorem to count particles and show that it fails in general for the Mott state. The failure stems from the divergent self energy that underlies Mottness. When such a divergence is present, charged degrees of freedom are present that have no particle interpretation. I will argue that such excitations are governed by a non-trivial IR fixed point and the propagator of which is of the unparticle form proposed by Georgi. I will show how a gravity dual can be used to determine the scaling dimension of the unparticle propagator. I will close by elucidating a possible superconducting instability of unparticles and demonstrate that unparticle stuff is likely to display fractional statistics in the dimensionalities of interest for strongly correlated electron matter. Time permitting, an underlying theory of the strongly coupled fixed point will be outlined.

Michael Stone, University of Illinois

Quantum and Classical Anomalies

I will begin reviewing the Callan-Harvey mechanism of anomaly inflow with particular focus on topological edge states and show how the inflow picture naturally converts the non-covariant "consistent" gauge anomaly of Bardeen and Zumino to the more physical "covariant" anomaly. I will then discuss some recent derivations of the covariant form of the gauge anomaly from classical phase space flows.

Jeffrey Teo, University of Illinois

Twist Defects in Topological Systems with Anyonic Symmetries

Twist defects are point-like objects that support robust non-local storage of quantum information and non-abelian unitary operations. Unlike quantum deconfined anyonic excitations, they rely on symmetry rather than a non-abelian topological order. Zero energy Majorana bound states can arise at lattice defects, such as disclinations and dislocations, in a topological crystalline superconductor. More general parafermion bound state can appear as twist defects in a topological phase with an anyonic symmetry, such as a bilayer fractional quantum Hall state and the Kitaev toric code. They are however fundamentally different from quantum anyonic excitations in a true topological phase. This is demonstrated by their unconventional exchange and braiding behavior, which is characterized by a modified spin statistics theorem and modular invariance.

Twist defects are point-like objects that support robust non-local
storage of quantum information and non-abelian unitary operations.
Unlike quantum deconfined anyonic excitations, they rely on symmetry
rather than a non-abelian topological order. Zero energy Majorana bound
states can arise at lattice defects, such as disclinations and
dislocations, in a topological crystalline superconductor. More general
parafermion bound state can appear as twist defects in a topological

I will begin reviewing the Callan-Harvey mechanism of anomaly inflow
with particular focus on topological edge states and show how the
inflow picture naturally converts the non-covariant "consistent"
gauge anomaly of Bardeen and Zumino to the more physical "covariant"
anomaly. I will then discuss some recent derivations of the covariant
form of the gauge anomaly from classical phase space flows.

When proximity coupled to s-wave superconductors, quantum wires can
support effective p-wave superconductivity under appropriate
circumstances. The p-wave state has Majorana states at the wire ends
which can store quantum information. I will discuss some properties of
Majorana states formed in oxide and semiconductor quantum wires,
including superconducting state phase diagrams as a function of
spin-orbit coupling strength, Fermi energy, and external magnetic field
strength, and Majorana exchange properties.

We employ holographic techniques to study quantum quenches at finite
temperature, where the quenches involve varying the coupling of the
boundary theory to a relevant operator with an arbitrary conformal
dimension. The evolution of the system is studied by evaluating the
expectation value of the quenched operator and the stress tensor
throughout the process. The time dependence of the new coupling is
characterized by a fixed timescale and the response of the observables

At a quantum critical point (QCP) in two or more spatial dimensions,
leading-order contributions to the scaling of entanglement entropy
typically follow the "area" law, while sub-leading behavior contains
universal physics. Different universal functions can be access through
entangling subregions of different geometries. For example, for
polygonal shaped subregions, quantum field theories have demonstrated
that the sub-leading scaling is logarithmic, with a universal
coefficient dependent on the number of vertices in the polygon.

One of the open problems in strong correlation physics is whether or not
Luttinger's theorem works for doped Mott insulators, particularly in
the pseudo gap regime where the pole-like excitations form only a Fermi
arc. I will begin this talk by using this theorem to count particles and
show that it fails in general for the Mott state. The failure stems
from the divergent self energy that underlies Mottness. When such a
divergence is present, charged degrees of freedom are present that have